Integrate the following: 1. fxsinxdx 2. fæcos2xdx 3. fe sinxdx

Q: ind the equation of a line that passes through A(1,-1) and is perpendicular to the line (x,y) =…

A: The equation of a line that passes through A(1,-1) and is perpendicular to the line…

Q: Proceed as in this example to find the solution of the given initial-value problem. Evaluate the…

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Q: 3. Evaluate the double integrals. -1/2 (a) [fx(1+ y²) d4; R is the region in the first quadrant…

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Q: 5. How many solutions are there between planes P₁: 2x -y + 2z = 2 and P₂: -x +2y+z=1? If there…

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Q: 1. Given a. b. C. [(5x + + + + 1) dx Evaluate the indefinite integral above Evaluate the integral…

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Q: Solve the following: √ ( sin 3x e3x 0 + 2) dx + 2x³ sin 2x) dx 2. 3. f sec x (secx + tanx) dx 7.…

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Q: Find the domain and range of the function graphed below. Use interval notation. 5 4 3 2 1 -5 -4 -3 2…

A: To find the domain and range of the function graphed below. To use the interval notation.

Q: 4) Find the value of a for which the limit lim x-0 evaluate the limit. sin(ax)-sinx-x. x3 is finite…

A: find limit

Q: Find all the second partial derivatives. V = e4xey Vxx = V xy v Vyx Vyy = = ||

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Q: 2. A line passes through the points P(4, -3) and Q(6,2). Write the following equations of the line:…

A: A line passes throughvthe points P(4,-3) and Q(6,2). Write the following equations of line. A) a…

Q: [(3+y) -x³ (3+y)³] dx + x dy = 0

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Q: Repeated Irreducible Quadratic Factors: Examples 2x² +9 x4 + 10x² + 25 dx

A: The given integral is;  (2x2+9)/(x4+10x2+25).

Q: 6 = √² (6x - x²) dx = We now have Area = 16

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Q: 14) A 300-foot cable weighting 4 pounds per is hanging from which 300 feet Level. Find ground the…

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Q: sec ( =) af Given f = e - yt+y, find dy sec 21 ____=_=(4) tam(3) ²(3) __g²¹3-¹ (z+y+yn (y)] xe sec…

A: see below the answer and calculation

Q: d²y 1. dx² - dy - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: Evaluate the integral. 1 -3 6²3 16 + r² dr

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Q: ow that a differentiable function f decreases most rapidly at x in the direction opposite the…

A: To find the direction derivative.

Q: 37) 1 Solve the following simultaneous linear D.E. [D+1 12 [+1 10+2 5D=210) = (2-1)

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Q: Use implicit differentiation to find y' and then evaluate y' at (-1,1). 3 x Iny+4y= 2x³ y'l(-1,1)=…

A: We have given  xlny+4y=2x3  Find y' and y' at (-1,1)

Q: 14 Approximate (x²-6) dx using 4 rectangles. 2 It is approximatley (If necessary, round to two…

A: Please follow the next step.

Q: Find the general solutions of the system. 601 x' = 08 8 -4 x 01 4 x(t)=

A: The given system,x'=60108-4014x

Q: Find (-¹)(-5) using the Inverse Function Theorem, given that r(x) = −4x³ – 5x² – 7x – 11 . Note that…

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Q: How many paths spell MANAGE? A N A A E a) 15 b) 100 c) 10 d) 20 M ΣΖ A E N G A

A: Use: Pascal's method

Q: Solve the following differential equations of 3.x d'y dx² +9y2e³* +18x+18

A: We can solve as follows

Q: Give the domain and range. Then, use the graph to find (a) f( − 2), (b) f(0), (c) (1) and (d) any…

A: From the graph, notice that the function is defined on the interval -2,4and it takes value on the y…

Q: √x²+25 - dx= x X=5secØ and Ø = sec الخيار رقم 1 0 X=5tan and Ø = tan-¹) X=5sinØ and Ø = sin ||| خيار…

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Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

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Q: If g(x, y) = x² + y² - 6x, find the gradient vector Vg(1, 6). Vg(1, 6) =

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Q: Given the function f(x) = x² + Draw a sketch of the graph of f. 16 - X x>0

A: Follow the procedure given below.

Q: 3. Derivative of g(x) = 2x + xª − 7x² +3 b) 12x³+4x³ - 14x +3 c) 12x6 +4x² - 14x²_____d) 12x³+4x³ -…

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Q: -4 -3 -2 -1 0 3 4 1 2 Write an interval to describe the set of values shown above.

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Q: 6. Bonus ( OL Solve for m 50 11 10.31 ffm m(8xy + x?)dxdy=3, 0<y<x<1

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Q: ▪ Find equation of plane which is containing Points A(2,1,1) and B (7,5,2) and normal to 2 x - 3y -…

A: Please follow the next step.

Q: Solve the equation 2x-1= 3x+1 algebraically.

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Q: 5a) Suppose y = f(g(x)). State the chain rule. That is, what is y' = dy/dx? Now, suppose f(x) =…

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Q: Hi, it is (-3)^n not (-2)^n

A: The given power series,∑n=0∞n2-n2nx+1n

Q: [x² (-2 + x² )* dx

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Q: Use the Table of Integrals to evaluate the integral. dx S ex(5 + 10e* Select the correct answer. -X…

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Q: Find the area of the shaded region. r = 1 + cos 0

A: Here, the given curves are r=1+cos θ &amp; r=3 cos θ First of all find the intersection points of…

Q: Calculus I In the exercise f(x)= cos x + sin x; [0,2pi], find the following 1.) Search for…

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Q: Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve,    r=sinθ+3cosθ, θ=π2

Q: If y₁ and y2 are linearly independent solutions of ty" + 3y + testy = 0 and if W(y₁, y₂)(1) = 4,…

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Q: IF x=t, y=t², 2= 2/3 t3 and r is the position vector, denoted by r=ti + t²j + 3/23 t²³³ k dT @ Find:…

A: Acccording to question,Given equations,x = ty = t2andz = 23t3andr = t i^ + t2 j^ +  23t3 k^

Q: Determine whether the given sequence converges or diverges. If it converges, calculate its limit. An…

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Q: coplanar.

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Q: What is the area of the region bounded by the curves y = sinx, y = cosx, x=0, and x=π/4. Round the…

A: What is the area of the region bounded by the curves y = sinx, y = cosx, x=0, and x=π/4. Round the…

Q: Find the producers' surplus at a price level of p = $61 for the price-supply equation below. p=…

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